Journal
ANIMAL BEHAVIOUR
Volume 84, Issue 6, Pages 1523-1531Publisher
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1016/j.anbehav.2012.09.026
Keywords
Bradley-Terry; goodness of fit; linearity; paired comparisons; ranking; rhesus macaque
Categories
Funding
- National Science Foundation [DMS-1007219]
- National Institutes of Health [R24 RR024396]
- Direct For Mathematical & Physical Scien [1007219] Funding Source: National Science Foundation
- Division Of Mathematical Sciences [1007219] Funding Source: National Science Foundation
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The construction of dominance hierarchies for animal societies is an important aspect of understanding the nature of social relationships, and the models to calculate dominance ranks are many. However, choosing the appropriate model for a given data set may appear daunting to the average behaviourist, especially when many of these models assume linearity of dominance. Here, we present a method to test whether or not a data set fits the assumption of linearity using the Bradley-Terry model as a representative of the class of models that assume linearity. Our method uses the geometry of a posterior distribution of possible rankings given the data by using a random walk on this distribution. This test is intuitive, efficient, particularly for large number of individuals, and represents an improvement over previous linearity tests because it takes into account all information (i.e. both linear and apparently circular or nonlinear information) from the data with few restrictions due to high dimensionality. Such a test is not only useful in determining whether a linear hierarchy is relevant to a given animal society, but is necessary in justifying the results of any analysis for which the assumption of linearity is made, such as the Bradley-Terry model. If the assumption of linearity is not met, other methods for ranking, such as the beta random field method proposed by Fushing et al. (2011, PLoS One, 6, e17817) should be considered. (C) 2012 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved.
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